Find the Value
\[ a^2+b^2+c^2=16 \]
\[ ab+bc+ca=10 \]
Find:
\[ a+b+c \]
Solution:
Using identity:
\[ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \]
\[ (a+b+c)^2 = 16+2(10) \]
\[ (a+b+c)^2 = 16+20 \]
\[ (a+b+c)^2 = 36 \]
\[ a+b+c = \pm 6 \]
\[ a^2+b^2+c^2=16 \]
\[ ab+bc+ca=10 \]
Find:
\[ a+b+c \]
Using identity:
\[ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \]
\[ (a+b+c)^2 = 16+2(10) \]
\[ (a+b+c)^2 = 16+20 \]
\[ (a+b+c)^2 = 36 \]
\[ a+b+c = \pm 6 \]